Graph Neural Networks with Low-rank Learnable Local Filters

For the classification of graph data consisting of features sampled on an irregular coarse mesh like landmark points on face and human body, graph neural network (gnn) models based on global graph Laplacians may lack expressiveness to capture local features on graph. The current paper introduces a new gnn layer type with learnable low-rank local graph filters, which significantly reduces the complexity of traditional locally connected gnn. The architecture provides a unified framework for both spectral and spatial convolutional gnn constructions. The new gnn layer is provably more expressive than gnn based on global graph Laplacians, and to improve model robustness, regularization by local graph Laplacians is introduced. The representation stability against input graph data perturbation is theoretically proved, making use of the graph filter locality and the local graph regularization. Experiments on spherical mesh data, real-world facial expression recognition/skeleton-based action recognition data, and data with simulated graph noise show the empirical advantage of the proposed model.